Intermittent Behaviors in Coupled Piecewise Expanding Map Lattices

In this paper,we propose a new method to study intermittent behaviors of coupled piecewise-expanding map lattices.We show that the successive transition between ordered and disordered phases occurs for almost every orbit when the coupling is small.That is,lim inf n→∞∑1≤i,j≤m|x_(i)(n)−x_(j)(n)|=0,lim sup n→∞∑1≤i,j≤m|x_(i)(n)−x_(j)(n)|≥c_(0)>0,where xi(n)correspond to the coordinates of m nodes at the iterative step n.Moreover,when the uncoupled system is generated by the tent map and the lattice consists of two nodes,we prove a phase transition occurs between synchronization and intermittent behaviors.That is,limn→∞|x_(1)(n)−x_(2)(n)|=0 for c−1/2<1/4 and intermittent behaviors occur for|c−1/2|>1/4,where 0≤c≤1 is the coupling.